Related papers: Time-ordering and a generalized Magnus expansion
Based on the assumption that time evolves only in one direction and mechanical systems can be described by Lagrangeans, a dynamical C*-algebra is presented for non-relativistic particles at atomic scales. Without presupposing any…
We present an exact expansion of the master equation for an open quantum system. The resulting equation is time local and enables us to calculate clearly defined higher order corrections to the Born-Markov approximation. In particular, we…
In this note, we provide an overarching analysis of primal-dual dynamics associated to linear equality-constrained optimization problems using contraction analysis. For the well-known standard version of the problem: we establish…
The time-ordered exponential representation of a complex time evolution operator in the interaction picture is studied. Using the complex time evolution, we prove the Gell-Mann -- Low formula under certain abstract conditions, in…
The time-ordered exponential is defined as the function that solves a system of coupled first-order linear differential equations with generally non-constant coefficients. In spite of being at the heart of much system dynamics, control…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
We review and provide simplified proofs related to the Magnus expansion, and improve convergence estimates. Observations and improvements concerning the Baker--Campbell--Hausdorff expansion are also made. In this Part IIA, we investigate…
We analyze the relation between the concept of auxiliary variables and the Inverse problem of the calculus of variations to construct a Lagrangian from a given set of equations of motion. The problem of the construction of a consistent…
New directions in research on master equations are showcased by example. Magnus expansions, time-varying rates, and pseudospectra are highlighted. Exact eigenvalues are found and contrasted with the large errors produced by standard…
We prove under certain assumptions that there exists a solution of the Schrodinger or the Heisenberg equation of motion generated by a linear operator H acting in some complex Hilbert space H, which may be unbounded, not symmetric, or not…
In it's usual presentation, classical mechanics appears to give time a very special role. But it is well known that mechanics can be formulated so as to treat the time variable on the same footing as the other variables in the extended…
The classical linear ordering problem seeks a single ranking representing a given preference matrix. While suitable for homogeneous populations, it fails when observed preferences arise from several latent groups with distinct ranking…
We consider the problem of learning the evolution operator for the time-dependent Schr\"{o}dinger equation, where the Hamiltonian may vary with time. Existing neural network-based surrogates often ignore fundamental properties of the…
The time-ordered exponential of a time-dependent matrix $\mathsf{A}(t)$ is defined as the function of $\mathsf{A}(t)$ that solves the first-order system of coupled linear differential equations with non-constant coefficients encoded in…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…
We solve the time evolution of a nonlinear optomechanical Hamiltonian with arbitrary time-dependent mechanical displacement, mechanical single-mode squeezing and a time-dependent optomechanical coupling up to the solution of two…
Canonical quantization applied to closed systems leads to static equations, the Wheeler-deWitt equation in Quantum Gravity and the time independent Schr\"odinger equation in Quantum Mechanics. How to restore time is the Problem of Time(s).…
The ``time-evolution operator'' in mechanics is a powerful tool which can be geometrically defined as a vector field along the Legendre map. It has been extensively used by several authors for studying the structure and properties of the…
In this work we show how the concept of majorization in continuous distributions can be employed to characterize chaotic, diffusive and quantum dynamics. The key point lies in that majorization allows to define an intuitive arrow of time,…
Operator-ordering in quantum cosmology is a major as-yet unsettled ambiguity with not only formal but also physical consequences. We determine the Lagrangian origin of the conformal invariance that underlies the conformal operator-ordering…